scholarly journals Mean-square upper bound of Hecke $L$-functions on the critical line.

2003 ◽  
Vol Volume 26 ◽  
Author(s):  
A Sankaranarayanan
Keyword(s):  
Cusp Form ◽  
Upper Bound ◽  
Critical Line ◽  
Congruence Subgroup ◽  
Mean Square ◽  
Absolute Value ◽  
International Audience ◽  
The Mean ◽  
The Absolute

International audience We prove the upper bound for the mean-square of the absolute value of the Hecke $L$-functions (attached to a holomorphic cusp form) defined for the congruence subgroup $\Gamma_0 (N)$ on the critical line uniformly with respect to its conductor $N$.

scholarly journals The Barban-Vehov Theorem in Arithmetic Progressions

2019 ◽  
Author(s):  
V Kumar Murty
Keyword(s):  
Asymptotic Formula ◽  
Arithmetic Progression ◽  
Upper Bound ◽  
Arithmetic Progressions ◽  
Mean Square ◽  
Titchmarsh Theorem ◽  
International Audience ◽  
The Mean ◽  
Selberg's Sieve

International audience A result of Barban-Vehov (and independently Motohashi) gives an estimate for the mean square of a sequence related to Selberg's sieve. This upper bound was refined to an asymptotic formula by S. Graham in 1978. In 1992, I made the observation that Graham's method can be used to obtain an asymptotic formula when the sum is restricted to an arithmetic progression. This formula immediately gives a version of the Brun-Titchmarsh theorem. I am taking the occasion of a volume in honour of my friend S. Srinivasan to revisit and publish this observation in the hope that it might still be of interest.

scholarly journals On an exponential sum involving the Möbius function

2005 ◽  
Vol Volume 28 ◽  
Author(s):  
H. Maier ◽  
A Sankaranarayanan
Keyword(s):  
Upper Bound ◽  
Exponential Sum ◽  
Möbius Function ◽  
Absolute Value ◽  
Mobius Function ◽  
International Audience ◽  
The Absolute

International audience In this paper we study the upper bound for the absolute value of the exponential sum related to the Möbius function unconditionally and present some interesting applications also.

scholarly journals The Saddle Point Method for the Integral of the Absolute Value of the Brownian Motion

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Leonid Tolmatz
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Saddle Point ◽  
Point Method ◽  
Saddle Point Method ◽  
Tail Asymptotics ◽  
Absolute Value ◽  
Exact Tail Asymptotics ◽  
International Audience ◽  
The Absolute

International audience The distribution function of the integral of the absolute value of the Brownian motion was expressed by L.Takács in the form of various series. In the present paper we determine the exact tail asymptotics of this distribution function. The proposed method is applicable to a variety of other Wiener functionals as well.

scholarly journals The Hodge Structure of the Coloring Complex of a Hypergraph (Extended Abstract)

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Sarah C Rundell ◽  
Jane H Long
Keyword(s):  
Euler Characteristic ◽  
Homology Group ◽  
Hodge Structure ◽  
Hodge Decomposition ◽  
Simple Graph ◽  
Absolute Value ◽  
International Audience ◽  
The Absolute ◽  
Nous Examinons ◽  
Coloring Complex

International audience Let $G$ be a simple graph with $n$ vertices. The coloring complex$ Δ (G)$ was defined by Steingrímsson, and the homology of $Δ (G)$ was shown to be nonzero only in dimension $n-3$ by Jonsson. Hanlon recently showed that the Eulerian idempotents provide a decomposition of the homology group $H_{n-3}(Δ (G))$ where the dimension of the $j^th$ component in the decomposition, $H_{n-3}^{(j)}(Δ (G))$, equals the absolute value of the coefficient of $λ ^j$ in the chromatic polynomial of $G, _{\mathcal{χg}}(λ )$. Let $H$ be a hypergraph with $n$ vertices. In this paper, we define the coloring complex of a hypergraph, $Δ (H)$, and show that the coefficient of $λ ^j$ in $χ _H(λ )$ gives the Euler Characteristic of the $j^{th}$ Hodge subcomplex of the Hodge decomposition of $Δ (H)$. We also examine conditions on a hypergraph, $H$, for which its Hodge subcomplexes are Cohen-Macaulay, and thus where the absolute value of the coefficient of $λ ^j$ in $χ _H(λ )$ equals the dimension of the $j^{th}$ Hodge piece of the Hodge decomposition of $Δ (H)$. Soit $G$ un graphe simple à n sommets. Le complexe de coloriage $Δ (G)$ a été défini par Steingrímsson et Jonsson a prouvé que l'homologie de $Δ (G)$ est non nulle seulement en dimension $n-3$. Hanlon a récemment prouvé que les idempotents eulériens fournissent une décomposition du groupe d'homologie $H_{n-3}(Δ (G))$ où la dimension de la $j^e$ composante dans la décomposition de $H_{n-3}^{(j)}(Δ (G))$ est égale à la valeur absolue du coefficient de $λ ^j$ dans le polynôme chromatique de $G, _{\mathcal{χg}}(λ )$ . Soit H un hypergraphe à $n$ sommets. Dans ce texte, nous définissons le complexe de coloration d'un hypergraphe $Δ (H)$ et nous prouvons que le coefficient de $λ ^j$ dans $χ _H(λ )$ donne la caractéristique d'Euler du $j^e$ sous-complexe de Hodge dans la décomposition de Hodge de Δ (H). Nous examinons également des conditions sur un hypergraphe H pour lesquelles les sous-complexes de Hodge sont Cohen-Macaulay. Ainsi la valeur absolue du coefficient de $λ ^j$ in $χ _H(λ )$ est égale à la dimension du $j^e$sous-complexe de Hodge dans la décomposition de Hodge de $Δ (H)$.

scholarly journals Measurements of CFC-11, CFC-12, and HCFC-22 total columns in the atmosphere at the St. Petersburg site in 2009–2019

2020 ◽  
Author(s):  
Alexander Polyakov ◽  
Anatoly Poberovsky ◽  
Maria Makarova ◽  
Yana Virolainen ◽  
Yuri Timofeyev
Keyword(s):  
Seasonal Variability ◽  
Climate Model ◽  
Independent Data ◽  
Mean Values ◽  
Absolute Value ◽  
Qualitative And Quantitative ◽  
Observational Site ◽  
Retrieval Strategies ◽  
The Mean ◽  
The Absolute

Abstract. The retrieval strategies for deriving the atmospheric total columns (TCs) of CFC-11 (CCl3F), CFC-12 (CCl2F2), and HCFC-22 (CHClF2) from ground–based measurements of IR solar radiation have been improved. We demonstrate the advantage of using the Tikhonov-Phillips regularization approach for solving the inverse problem of the retrieval of these gases and give the optimized values of regularization parameters. The estimates of relative systematic and random errors amount to 7.61 % and 3.08 %, 2.24 % and 2.40 %, 5.75 % and 3.70 %, for CFC-11, CFC-12, and HCFC-22, respectively. We analyze the time series of the TCs and mean molar fractions (MMFs) of CFC-11, CFC-12, and HCFC-22 measured at the NDACC site St. Petersburg located near Saint Petersburg, Russia for the period of 2009–2019. Mean values of the MMFs for CFC-11, CFC-12, and HCFC-22 total 225, 493, and 238 pptv, respectively. Estimates of the MMFs trends for CFC-11, CFC-12, and HCFC-22 account for −0.40 ± 0.07 %/yr, -0.49  ±0.05 %/yr, and 2.12±0.13 %/yr, respectively. We have compared the mean values, trends and seasonal variability of CFC-11, CFC-12, and HCFC-22 MMFs measured at the St. Petersburg site in 2009–2019 to that of 1) near–ground volume mixing ratios (VMRs) measured at the observational site Mace Head, Ireland (GVMR); 2) the mean in the 8–12 km layer VMRs measured by ACE–FTS and averaged over 55–65° N latitudes (SVMR); and the MMFs of the Whole Atmosphere Community Climate Model for the St. Petersburg site (WMMF). The means of the MMFs are less than that of the GVMR for CFC-11 by 9 pptv (3.8 %), for CFC-12 by 24 pptv (4.6 %); for HCFC-22, the mean MMFs does not differ significantly from the mean GVMR. The absolute value of the trend estimates of the MMFs is less than that of the GVMR for CFC-11 (−0.40 vs −0.53 %/yr) and CFC-12 (−0.49 vs −0.59 %yr); the trend estimate of the HCFC-22 MMFs does not differ significantly from that of the GVMR. The seasonal variability of the GVMR for all three gases is much lower than the MMFs variability. The means of the MMFs are less than that of the SVMR for CFC-11 by 10 pptv (4.3 %), for CFC-12 by 33 pptv (6.3 %), and for HCFC-22 by 2 pptv (0.8 %). The absolute value of the trend estimates of the MMFs is less than that of the SVMR for CFC-11 (−0.40 vs −0.63 %/yr) and CFC-12 (−0.49 vs −0.58 %/yr); the trend estimate of the HCFC-22 MMFs does not differ significantly from that of the SVMR. The MMF and SVMR values show nearly the same qualitative and quantitative seasonal variability for all three gases. The means of the MMFs are greater than that of the WMMF for CFC-11 by 22 pptv (10 %), for CFC-12 by 15 pptv (3.1 %), and for HCFC-22 by 23 pptv (10 %). The absolute value of the trend estimates of the MMFs is less than that of the WMMF for CFC-11 (−0.40 vs −1.68 %/yr), CFC-12 (−0.49 vs −0.84 %/yr), and HCFC-22 (2.12 %/yr vs 3.40 %/yr). The MMFs and WMMF values show nearly the same qualitative and quantitative seasonal variability for CFC-11 and CFC-12, whereas the seasonal variability of the WMMF for HCFC-22 is essentially less than that of the MMFs. In general, the comparison of the MMFs with the independent data shows a good agreement of their means within the systematic error of considered measurements. The observed trends over the St. Petersburg site demonstrate the smaller decrease rates for CFC-11 and CFC-12 TCs than that of the independent data, and the same decrease rate for HCFC-22. The suggested retrieval strategies can be used for analysis of the IR solar spectra measurements using Bruker FS125HR spectrometers, e.g. at other IRWG sites of the NDACC observational network.

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